Ruth Davidson said thousands of people are angry at Nicola Sturgeon’s administration for putting “its own narrow political interests before those of the wider country”.
But the SNP said Ms Davidson should be apologising for the “mess” her party has created with Brexit.
The claims come after Ms Sturgeon launched a “new conversation” on Scottish independence on Friday, with the aim of targeting up to two million voters before the end of November.
The SNP leader described it as the “biggest-ever political listening exercise”, which will seek views using a far-reaching survey and meetings across the country.
The First Minister stressed the initiative will not be a “rerun” of the 2014 arguments, which saw Scots vote by 55% to 45% to remain in the UK.
In a speech in Perth, Ms Davidson said: “Nicola Sturgeon said yesterday that she wants to listen to people who voted No in the hope of meeting their concerns. Well let me tell her how many of us feel.
“We do not look back at the referendum on independence with much in the way of nostalgia. It wasn’t ‘civic’ or ‘joyous’ as the SNP have claimed.
“Instead, we remember the division it caused, we remember the pain felt by many, and we remember the fear that our country was about to be split up.
“And we don’t want to put our country through it all again.”
She went on: “So if the First Minister wants to know the feelings of thousands of Scots across the country - I can give it to her right now.
“It is anger at an SNP Government which has both broken its word and decided to put its own narrow political interests before those of the wider country.
“And it is frustration that we have a nationalist administration which is acting like a drag on Scotland’s progress.
“Instead of a proper Government using new and existing powers to drive the country forward, we instead have a nationalist administration dragging Scotland backwards - allowing the lead weight of separatism to threaten our ambitions and hopes.”
The SNP branded the speech “arrogant hypocrisy” from the Tories.
A spokesman said: “It was Ruth Davidson who promised that ‘No means we stay’ in the EU and she should be apologising for the mess her party has now created with Brexit.
“People in Scotland remember very well the promises that the Tory-led No campaign made in the run up to the 2014 referendum - on shipbuilding, on the EU, on devolution and more - and they have watched as one-by-one these promises and pledges have been broken.
“Scotland faces being dragged out of the EU against our will by an increasingly right-wing, reactionary Tory party.
“It is only right that the Scottish Government examines all options to protect Scotland’s interests and maintain our place in the EU - including the possibility of a second independence referendum.”